Mode-selecting effects and coherence in hot-plasma x-ray lasers

The three-dimensional time-dependent set of Maxwell-Bloch equations for amplified spontaneous emission in diffraction-dominated (low Fresnel number) and small-gain systems is solved. The explicit form of the modes of radiation for gain and density profiles which are typical of hot-plasma x-ray-laser experiments is derived. The behavior of the excitation strengths of the modes is analyzed. It is found that, due to the combined effects of diffraction, refraction, and gain, the excitation strength is a more rapidly decreasing function of the mode number in systems with smaller Fresnel numbers. The behavior of coherence as a function of propagation length in systems with various Fresnel numbers is computed and analyzed.